## THERMAL SCIENCE

International Scientific Journal

### IDENTIFYING OF UNKNOWN SOURCE TERM FOR THE RAYLEIGH-STOKES PROBLEM

**ABSTRACT**

In this paper, we would like to briefly introduce some applications of fractional derivatives in the fields of heat and fluid-flows. However, our main focus is on study an inverse source problem for the Rayleigh-Stokes problem. The problem is severely ill-posed. We verify the ill-posedness of Problem 1, applying the modified Lavrentiev to construct a regularization from the exact data. After that, we established the convergent rate between the exact solution and its approximation. Furthermore, we have the estimate in Lq space.

**KEYWORDS**

PAPER SUBMITTED: 2022-02-25

PAPER REVISED: 2022-03-14

PAPER ACCEPTED: 2022-04-24

PUBLISHED ONLINE: 2023-04-08

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